Which product is negative?
(-3/8)(-5/7)(1/4)

(3/8)(-5/7)(-1/4)

(3/8)(5/7)(1/4)

(-3/8)(-5/7)(-1/4)

Given:

The x- intercepts of a parabola are (0,-6) and (0,4).

The parabola crosses the y- axis at -120.

Lucas said that an equation for the parabola is [tex]y=5x^2+10x-120[/tex] and that the coordinates of the vertex are (-1, -125).

To find:

Whether Lucas is correct or not.

Solution:

The x- intercepts of a parabola are (0,-6) and (0,4). It means (x+6) and (x-4) are the factors of the equation of the parabola.

[tex]y=a(x+6)(x-4)[/tex]             ...(i)

The parabola crosses the y- axis at -120. It means the equation of the parabola must be true for (0,-120).

[tex]-120=a(0+6)(0-4)[/tex]

[tex]-120=a(6)(-4)[/tex]

[tex]-120=-24a[/tex]

Divide both sides by -24.

[tex]\dfrac{-120}{-24}=a[/tex]

[tex]5=a[/tex]

Substituting [tex]a=5[/tex] in (i), we get

[tex]y=5(x+6)(x-4)[/tex]

[tex]y=5(x^2+6x-4x-24)[/tex]

[tex]y=5(x^2+2x-24)[/tex]

[tex]y=5x^2+10x-120[/tex]

So, the equation of the parabola is [tex]y=5x^2+10x-120[/tex].

The vertex of a parabola [tex]f(x)=ax^2+bx+c[/tex] is:

[tex]Vertex=\left(-\dfrac{b}{2a},f(-\dfrac{b}{2a})\right)[/tex]

In the equation of the parabola, [tex]a=5,b=10,c=-120[/tex].

[tex]-\dfrac{b}{2a}=-\dfrac{10}{2(5)}[/tex]

[tex]-\dfrac{b}{2a}=-\dfrac{10}{10}[/tex]

[tex]-\dfrac{b}{2a}=-1[/tex]

Putting [tex]x=-1[/tex] in the equation of the parabola, we get

[tex]y=5(-1)^2+10(-1)-120[/tex]

[tex]y=5-10-120[/tex]

[tex]y=-125[/tex]

So, the vertex of the parabola is at point (-1,-125).

Therefore, Lucas is correct.

Answer: Choice C. 32,768

Explanation:

2.5 hours = 2.5*60 = 150 minutes

150/10 = 15

There are 15 periods that are 10 minutes each in a 2.5 hour timespan.

y = a*b^x

y = 1*2^15

y = 32,768

If you started with a = 1 bacterium, then it will double a total of 15 times to end up with 32,768 bacteria after the 2.5 hour period.

Answer:

A. (-1, 3)

Step-by-step explanation:

When reflecting across the y-axis: (x, y) ⇒ (-x, y).

Therefore, A(1, 3) ⇒ A'(-1, 3).

Answer:

Step-by-step explanation:

Since the coordinates of P are (0, 1), this makes P the y-intercept of that line. The y-intercept exists where x = 0. And in the coordinate (0, 1), x does in fact equal 0.

Since the one coordinate given in Q is (?, 0), this means that Q is the x-intercept of the line. The x-intercept exists where y = 0. And in the coordinate (?, 0), y does in fact equal 0. So in order to solve for the x coordinate of Q, we plug in a 0 for y and solve for x:

3(0) - 4x = 12 and

-4x = 12 so

x = -3

Answer:

125 cm³

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Geometry

Volume of a Cube Formula: V = a³

Step-by-step explanation:

Step 1: Define

Identify variables

a = 5 cm

Step 2: Find Volume

Answer:

[tex]\huge\boxed{V=125cm^3}[/tex]

Step-by-step explanation:

The formula of a volume of a cube with edge [tex]a[/tex]:

[tex]V=a^3[/tex]

We have [tex]a=5cm[/tex].

Therefore the volume is:

[tex]V=(5cm)^3=5cm\cdot5cm\cdot5cm=125cm^3[/tex]

Answer:

x=5

Step-by-step explanation:

This is because the inscribed angle of the circle or angle EFG is equal to the twice of the degree of the arc EG. Therefore, we can create this equation:

12+40=2(8x+10)

12+40=16x+20

20=4x

x=5

Answer:

B=30mm

Step-by-step explanation:

According to the Question,

we have,  A parallelogram that has one side(A) 5 millimeters and the other side(C) 10 millimeters. A larger parallelogram has side one side(D) 15 millimeters.

The Enlargement Parallelogram And Original Parallelogram Sides Ratio Remain the same.

Therefore, A/C = D/B

5/10 = 15/B

B=150/5

B=30mm

Orders of Magnitude are in terms of scientific notation.

23,000 written in scientific notation is 2.3 x 10^4, it's magnitude is 4 ( the number 10 is raised to)

56 in scientific notation would be 5.6 x 10^1, its magnitude is 1.

4 - 1 = 3

2300 is 3 order of magnitudes larger.

The answer is 3.

9514 1404 393

Answer:

  p = 30

  angles 30°, 45°; exterior: 75°

Step-by-step explanation:

The exterior angle is equal to the sum of the remote interior angle:

  3p -15 = p + (p +15)

  p = 30 . . . . . . . . . . . . . add 15-2p

The interior angles are 30°, 45°; the exterior angle is 75°.

Answer:

B.

Step-by-step explanation:

m is the driving number in this system of numbers. whatever its value, all the others need to adjust to it.

c depends fully on m. if and when m increases, then also c has to increase.

Answer:

Multiply to -63

and add to -2

Step-by-step explanation:

I'm a genius.

Answer:

(x - 9)(x + 7)

Step-by-step explanation:

Given

x² - 2x - 63

Consider the factors of the constant term (- 63) which sum to give the coefficient of the x- term, that is

numbers that multiply to give - 63 and add to give - 2

The factors are - 9 and + 7 , since

- 9 × 7 = - 63 and - 9 + 7 = - 2 , then

x² - 2x - 63 = (x - 9)(x + 7) ← in factored form

Answer:

x>-1.25

Step-by-step explanation:

0.2x+4-3>-7-6.2x

0.2x+1>-7-6.2x

0.2x+6.2x>-7-1

6.4x>-8

x>-1.25

or x>-5/4,x>-1 1/4, xE(-1.25, infinite)

The solution to the inequality is x > -1.25.

The complete steps are:

the distributive property: 0.2x+4-3>-7-6.2x

Combine like terms: 0.2x+1>-7-6.2x

the addition property of inequality: 0.2x+6.2x +1 >-7 => 6.4x + 1 > –7

the subtraction property of inequality: 6.4x > -7 - 1 => 6.4x>-8

the division property of inequality: (6.4x)/6.4 > (-8)/6.4 => x>-1.25

Here, we have,

To solve the inequality 0.2(x + 20) - 3 > -7 - 6.2x,

let's go through the steps:

Step 1: Use the distributive property:

0.2x + 4 - 3 > -7 - 6.2x

Step 2: Combine like terms:

0.2x + 1 > -7 - 6.2x

Step 3: Use the addition property of inequality:

0.2x + 1 + 6.2x > -7

6.4x + 1 > -7

Step 4: Use the subtraction property of inequality:

6.4x > -7 - 1

6.4x > -8

Step 5: Use the division property of inequality:

Divide both sides of the inequality by 6.4 to isolate x:

(6.4x)/6.4 > (-8)/6.4

x > -8/6.4

Simplifying further, we have:

x > -1.25

Therefore, the solution to the inequality is x > -1.25.

To learn more on inequality click:

https://brainly.com/question/28841069

#SPJ5

Answer:

[see below]

Step-by-step explanation:

V = s^3

V = (x+4)^3

V = x^3 + 3x^2 * 4 + 3x * 4^2 + 4^3

V = x^3 + 12x^2 + 48x + 64

Hope this helps.

Answer:

(-1,1)

Step-by-step explanation:

(x,y), and X is one unit to the left (negative, or -), while Y is one unit up

Answer:

19.5 cm

Step-by-step explanation:

the remaining height = 1200 /(12×8)

= 1200/96 = 12.5 cm

so, the height of the tank = 7+ 12.5 = 19.5 cm

[tex]\displaystyle\bf \boxed{V=abh \ ; \ 1dm^3=1litre=1000cm^3} \\\\a=12cm \ ; \ b=8 cm ;\: h_1=7 \; ; \ h_0=h_1+h_2=?\\\\abh_2=1,2litre=1,2dm^3\ = 1200cm^3\\\\ 8\cdot 12 h_2=1200\\\\h_2=12.5 cm\: then \\\\h_0= 7+12,5=19,5 \\\\Answer : the \ height \ of \ the \ tank \ is \ 19,5 cm[/tex]

Answer: Approximately 0.667%

Work Shown:

2/300 = 1/150 = 0.00667 = 0.667%

So less than 1% of the chips are defective.

Answer:

$28

Step-by-step explanation:

Answer:

6=$3

5=$2

6x3=18

5x2=10

18+10= 28

=$28

Step-by-step explanation:

Answer:

I don't understand your question.............!

Step-by-step explanation:

Answer:

Hey, could you please add the number line to the question too

Answer:

a = 1000, p = 10

Step-by-step explanation:

Given

y = - 3lg x + lg a

in the form y = mx + c ( m is the slope and c the y- intercept )

From the graph

(a)

c = 3 , then

lg a = 3 , that is

a = 10³ = 1000

(b)

Replace x by p and y = 0 in the equation

0 = - 3lg p + 3 ( subtract 3 from both sides )

- 3 = - 3lg p ( divide both sides by - 3 )

1 = lg p

p = 10 [ [tex]log_{10}[/tex] 10 = 1 ]

Answer:

25 + 300 = 325

trousers: spent 30 (a pair of trousers = one unity of trousers)

shirts: spent 19 x 2 = 38

shoes: spent 40 x 2 = 80

80 + 38 + 30 = 148

325 - 148 = 177

She had $177,00 left.

hope it helps.

Also, I think that Brainly is an awesome app, but there's an app which is doing great work for me in maths, named Gauthmath. I will suggest it. Video concepts and answers from real tutors.

Answer:

x ≤ 3

Step-by-step explanation:

2(4+2x)≥5x+5

8+4x≥5x+5

4x-5x≥5-8

-x≥-3

x ≤ 3

[tex]\tt\displaystyle\2(4+2x)\geq 5x+5\\\\8+4x\geq 5x+5\\\\4x-5x\geq 5-8\\\\-x\geq -3\\\\x\leq 3 \\\\Answer: x\leq 3 \quad or \quad x\in(-\infty;3][/tex]

Answer:

10

Step-by-step explanation:

use a^2+b^2=c^2

6^2+8^2=c^2

100=c^2

sqrt it and you get 10 for AC and AC=DB

Answer:

according to Pythagoras theorem, c²=a²+b²

|AC|²=|AD|²+|DC|²

|AC|²=6²+8²

|AC|²=36+64

|AC|²=100

√|AC|²=√100

|AC|=10

Answer:

They are parallel so also -4/3

The polynomials f(x) = x^2 + bx + 400 have -20 as its only zero then the value of b is 40.

The polynomials f(x) = x^2 + bx + 400 have -20 as its only zero

Then x=-20

The zeros of a polynomial p(x) are all the x-values that make the polynomial equal to zero.

x=-20 is the zero of the given polynomial

Therefore it satisfies the given polynomial

[tex]f(-20)=(-20)^2+b(-20)+400[/tex]

[tex]0=400-20b+400\\800-20b=0\\-20b=-800\\b=\frac{-800}{-20} \\b=40[/tex]

Therefore the value of b is 40.

To learn more about the zeros of the polynomials visit:

https://brainly.com/question/12461081

Answer:

C) 3 times the sq root of 3

Step-by-step explanation:

In a right angle triangle, the COS is definned as the ajacent side over the hypotenuse. So

COS 60 = JK/JL

COS 60 = JK/(6*sq root 3)

.5 = JK/(6*3**1/2)

JK = .5 *(6*3**1/2)

JK = 3*3**1/2

The distance traveled depends on the amount of time Marlene rides her bike

The function f(t) = 16t represents the scenario

Answer:

options (2), (3) and (5)

Step-by-step explanation:

2.

the distance traveled depends upon the amount of time she rides her bike.

as she travels 16 miles in 1 hr. she'll ride 32 miles in 2 hrs. so all values of distance traveled by her depends upon the time she takes.

3.

yes the initial is 16 miles per hour as the output of 1hr will be 16 and that's what the initial value is 16 miles for one hour. or 16 miles per hour.

5.

f(t) = 16t represents the scenario

where f(t) will be the output of the function that is d, distance when the output is t that is time.

Answer:

A

Step-by-step explanation:

A central bank was needed to oversee monetary policy

Answer:A

Step-by-step explanation:

I did the test

Answer:

3rd option

Step-by-step explanation:

f(x) = 0 are the points on the x- axis where the graph crosses, the zeros

The graph crosses the x- axis at - 2 , 1 and 3